Answer: pi/3.
- A pi/6
- B pi/4
- C pi/3
- D pi/2
Correct answer: C. pi/3
Explanation: tan(pi/3) = sqrt(3), and pi/3 lies in the principal range, so tan-1(sqrt3) = pi/3.
The graph of sin⁻¹x is confined to a narrow domain [-1,1] (since sine itself only takes values in that range) and range [-π/2,π/2] (the principal value branch chosen to make sine one-one and invertible there).
Concept context
Restricting trig functions to make them invertible, the principal value branches of sin-inverse, cos-inverse, tan-inverse, and friends, and the key identities relating them.